IVP Annual Interest and return

(2) Suppose we invested $20,000 at an annual rate of 4% where interest is compounded continuously. (a) Write down an IVP that describes the amount of money y(t) that you will have in your account after t years. (b) Solve the IVP you obtained in (a) and compute how much money you expect to have in your account after 5 years. (c) Now let's assume that you want to make daily deposits to make the money grow faster. Let's start small and say we are going to make deposits that amount to $5,000 per year. Write down the IVP that models this new scenario. (d) Solve the IVP in (c) and compute how much money you expect to have in your account after 5 years in this new scenario. (e) Now, suppose you are saving money to start the process of buying a small house in 5 years. You are willing to increase your yearly deposits so you now deposit about $8,000 per year. How much money should you have in your account right now (that is, what should 9(0) be) in order for you to have at least $100,000 in your account in 5 years